Fractional-order interactive systems of calcium, IP3 and nitric oxide in neuronal cells

Abstract Calcium ions ( Ca 2 + ), 1, 4, 5-inositol trisphosphate ( IP 3 ), and nitric oxide ( NO ) function as signaling molecules and are crucial for controlling several physiological mechanisms in neuronal cells. Nevertheless, there is a lack of research investigating the interplay between Ca 2 + , IP 3 and NO in neuronal cells, in terms of fractional-order dynamics. The investigation of fractional-order interacting dynamical systems including calcium, IP 3 , and NO is of crucial significance as it sheds light on several phenomena such as superdiffusion and the emergence of cell memory exhibiting Brownian motion ( BM ) in neurons. These aspects have not yet been thoroughly examined in neurons. The theoretical framework employed in this study is a fractional model that describes the interacting calcium, IP 3 , and NO systems incorporating the nonlinear reaction-diffusion equations, fractional diffusion processes, and memory effects. The Crank-Nicholson ( CN ) method with the Grunwald technique is utilized to address the fractional-order space derivatives, while the L1 technique is applied to solve the fractional-order temporal derivatives. The Gauss-Seidel ( GS ) procedure is employed to solve the system of nonlinear equations governing the dynamics of Ca 2 + , IP 3 , and NO . The previously unexplored bidirectional feedback mechanisms between calcium and NO and calcium and IP 3 have been explored. The current study includes the incorporation of several critical parameters, including the voltage-gated calcium channel ( VGCC ), Orai channel, IP 3 -receptor ( IP 3 R ), Sarcoendoplasmic Reticulum Calcium ATPase ( SERCA ) pump, leak, plasma membrane Ca 2 + ATPase ( PMCA ) channel, sodium-calcium exchanger ( NCX ), ryanodine receptor ( RyR ), and [NO] -dependent Ca 2 + flux. The numerical findings show that superdiffusion and cell memory with several cellular mechanisms significantly affect the regulation of the interacting nonlinear calcium, IP 3 , and NO dynamical systems in neuronal cells. Neurotoxic events potentially contributing to disease-related conditions such as Alzheimer’s may result from dysfunction in the superdiffusion and memory of signaling ions and molecules, as well as the cellular mechanisms within neurons.